Results 21 to 30 of about 97,370 (265)
On Transitive Permutation Groups
LMS Journal of Computation and Mathematics, 1998 AbstractWe assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.
John H. Conway +2 more
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On the Group of Alternating Colored Permutations [PDF]
The Electronic Journal of Combinatorics, 2014 The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\mathbb{Z}_r \wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation.
Eli Bagno, David Garber, Toufik Mansour
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Permutation codes over Sylow 2-subgroups $Syl_2(S_{2^n})$ of symmetric groups $S_{2^n}$
Researches in Mathematics, 2021 The permutation code (or the code) is well known object of research starting from 1970s. The code and its properties is used in different algorithmic domains such as error-correction, computer search, etc.
V.A. Olshevska
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Sync-Maximal Permutation Groups Equal Primitive Permutation Groups [PDF]
, 2021 The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational problems related to synchronization and to the length of synchronizing words.
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Solvable intransitive permutation groups with constant movement [PDF]
Journal of Mahani Mathematical ResearchIn this paper, all solvable intransitive permutation groups with constant movement are classified and we show that they are one of the following groups: a cyclic $p$-group, an elementary abelian $p$-group, a Frobenius group of order 12 or a Frobenius ...
Mehdi Rezaei +2 more
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The Fixity of Permutation Groups
Journal of Algebra, 1995 By definition, the fixity of a finite permutation group \(G\) is the maximal number of fixed points of a non-identity element of \(G\); so if \(f\) denotes the fixity of \(G\) and \(n\) the degree of \(G\) then \(n-f\) is the minimal degree of \(G\). The authors prove some general theorems on transitive permutation groups \(G\) with given fixity \(f>0\)
Saxl, J., Shalev, A.
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On the Movement of a Permutation Group
Journal of Algebra, 1999 If \((G,\Omega)\) is a permutation group, then the movement \(\text{move}(G)\) is the supremum of \(\{|\Gamma^g\setminus\Gamma|:\Gamma\subseteq\Omega,\;g\in G\}\). If \(G\) has no fixed points, \(n:=|\Omega|\), and \(\text{move}(G)=m\) is finite, then \(n\leq 5m-2\), by a result of \textit{C. E. Praeger} [J. Algebra 144, No.
Neumann, P, Praeger, C
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Signed graphs and signed cycles of hyperoctahedral groups
Electronic Journal of Graph Theory and Applications, 2023 For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices.
Ryo Uchiumi
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On the diameter of permutation groups
European Journal of Combinatorics, 1992 The authors give an asymptotic universal upper bound for the diameter of all Cayley graphs of all permutation groups of degree \(n\), namely, they show that for any set of permutations \(S\) in \(S_ n\), every permutation in the subgroup generated by \(S\) can be expressed as a product of length at most \(\exp((n\cdot\ln n)^{1/2}(1+o(1)))\) of factors ...
László Babai, Ákos Seress
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Cubic Cayleygraphs with small diameter. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we apply Polya's Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group.
Eugene Curtin
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